Homoclinic orbits in a parametrized saddle-focus system

DOI10.1016/0167-2789(93)90285-9zbMath0783.58062OpenAlexW1977381361MaRDI QIDQ1312461

John A. Feroe

Publication date: 31 January 1994

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(93)90285-9

zbMATH Keywords

eigenvalueshomoclinic orbitequilibrium pointnerve axon equations

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Equilibrium statistical mechanics (82B99) Ergodic theorems, spectral theory, Markov operators (37A30)

Related Items (11)

Bifurcations of systems with structurally unstable homoclinic orbits and moduli of \(\Omega\)-equivalence ⋮ One mechanism of appearance of a spiral quasiattractor involving heteroclinic contours ⋮ Basic structures of the Shilnikov homoclinic bifurcation scenario ⋮ Shilnikov homoclinic orbit bifurcations in the Chua’s circuit ⋮ Bifurcations for heteroclinic orbits of a periodic motion and a saddle-focus and dynamical chaos ⋮ Global invariant manifolds near a Shilnikov homoclinic bifurcation ⋮ Existence of heterodimensional cycles near shilnikov loops in systems with a \(\mathbb{Z}_2\) symmetry ⋮ On Bifurcations Leading to Chaos in Chua's Circuit ⋮ On Bifurcations Leading to Chaos in Chua's Circuit ⋮ Scientific heritage of L. P. Shilnikov ⋮ Shilnikov chaos, Filippov sliding and boundary equilibrium bifurcations

Cites Work

• Unnamed Item
• Local and global behavior near homoclinic orbits
• Stability of Double-Pulse Solutions in Nerve Axon Equations
• Double Impulse Solutions in Nerve Axon Equations
• Existence of Traveling Wave Trains in Nerve Axon Equations
• Multiple impulse solutions to McKean's caricature of the nerve equation. II. Stability
• Existence and Stability of Multiple Impulse Solutions of a Nerve Equation
• Single and Multiple Pulse Waves for the FitzHugh–Nagumo
• On an Ordinary Differential Equation Involving a Convex Function
• A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE
• Multiple impulse solutions to McKean's caricature of the nerve equation. I—existence

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